Hostname: page-component-745bb68f8f-kw2vx Total loading time: 0 Render date: 2025-01-22T08:06:25.548Z Has data issue: false hasContentIssue false
  • English
  • Français

Tree sign pattern matrices that require zero eigenvalues

Published online by Cambridge University Press:  17 April 2009

Wei-Hsu Chen  and
Mao-Ting Chien
Wei-Hsu Chen
Affiliation:
Department of Mathematics, Soochow University, Taipei, Taiwan 11102
Mao-Ting Chien
Affiliation:
Department of Mathematics, Soochow University, Taipei, Taiwan 11102
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We characterise tree sign pattern matrices that require at least k zero eigenvalues, and exactly k zero eigenvalues.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 55 , Issue 1 , February 1997 , pp. 81 - 88
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Brualdi, R. and Ryser, H.J., Combinatorial matrix theory (Cambridge Univ. Press., Cambridge, 1991).CrossRefGoogle Scholar
[2]Eschenbach, C.A. and Johnson, C.R., ‘Several open problems in qualitative matrix theory involving eigenvalue distribution’, Linear and Multiliner Algebra 24 (1988), 79–80.Google Scholar
[3]Eschenbach, C.A. and Johnson, C.R., ‘Sign patterns that require real, nonreal or pure imaginary eigenvalues’, Linear and Multilinear Algebra 29 (1991), 299–311.Google Scholar
[4]Eschenbach, C.A. and Johnson, C.R., ‘Sign patterns that require repeated eigenvalues’, Linear Algebra Appl. 190 (1993), 169–179.Google Scholar
[5]Maybee, J. and Quirk, J., ‘Qualitative problems in matrix theory’, SIAM Rev. 11 (1969), 30–51.CrossRefGoogle Scholar
[6]Quirk, J. and Ruppert, R., ‘Qualitative economics and the stability of equilibrium’, Rev. Econom. Stud. 32 (1965), 311–326.CrossRefGoogle Scholar
[7]Yeh, L., ‘Sign pattern matrices that allow a nilpotent matrix’, Bull. Austr. Math. Soc. 53 (1996), 189–196.Google Scholar